Expert: James J. Kovalcin - 3/6/2006

Question
I don't seem to quite understand diffraction gratings with white light...
Here is how I have tried to think about it:
If you have a diffraction grating with 4 slits creating 4 coherent sources S1 S2 S3 S4 respectivly.
"at the central maximum there is no path difference" but light from S1 has travelled further than light from S2 so how can pathd = 0, UNLESS it means that the 2 halves of the grating are in phase with each other ie) for a central max, S1 is in phase with S4 and S2 is in phase with S3. which would explain why the zeroth maximum appears in the center (effectivly a line of symmetry). I suppose if you only had 3 sources (S1 S2 S3 respectivly) the central maximum would appear directly opposite S2.
Now, if we go back to the 4 slit grating, the central max appears half way in between S1 S2 S3 S4, but if we covered up S3 and S4 wouldn't the central max jump to between S1 and S2?

We did an experiment measuring the refractive index of a semicircular perspex box (experiment close to the one on this website http://physics.montana.edu/demonstrations/apparatus/6_optics/demos/blackboardopt

We used white light and shone it through the block and the white light was refracted (refractive index = 1.4) but why didn't the white light split up into its component colors like it does when shone through a prism?

Thanks again for your help
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Followup To
Question -
If you have a diffraction grating with 2 slits and you pass white light through it there is one point in the centre of the screen where the path difference of the 2 sources is zero (central order maximum) so white light is reformed there, but if you have a diffraction grating with say 600 slits why will there NOT be 300 areas of white light? (ie 300 1st order maximums for each pair of slits?)

All electromagnetic waves travel at 3x10^8m/s in a vacuum, but how can we give a speed of light in glass (it would depend on the light used as red light travels faster than violet light because violet light refracts more)?
When we say "the speed of light in glass" are we meaning the speed of white light?

Thank you for your help.
Answer -
The bright interference bands you are refering to exist only where light waves come together IN PHASE!. As you have already noted this is what happens in the central maximum. There are, however, other locations where light waves will arrive in phase. In particular, constructive interference will occur any time two waves arrive at a particular location such that the two waves arrive an integer number of wavelengths out of phase. For example, if two waves arrive at a point exactly one wavelength out of phase, they are, in fact, exactly in phase! These waves will constructively interfere. The same can be said for two waves that arrive 2 wavelengths, 3 wavelengths, 4 wavelengths etc. out of phase. The angle at which this occurs is given by
n*lambda=d*sin(theta) where
n - how many wavelengths out of phase the waves will be
lambda - the wavelength of the individual waves
d - the distance between the centers of the adjacent slits
theta - the angle at which the bright maximum will occur
You can predict the number of maxima that will occur by assuming an angle of 90 degrees and dividing the distance between the slits by the wavelength of the wave.
n=d/lambda.
The number of slits just doesn't come into it [although the spacing d between the slits does!  

Answer
The grating works because the path length different from each slit to a particular bright fringe will be exactly one length. The slits in a diffraction grating are extremely close together. For example consider a diffraction grating with 5 evenly spaced slits. The center slit will generate an interference fringe dead center. The slits, one on either side of the central slit, will be exactly 1 wavelength farther from the central antinode. The slits 2 from the central slit will pass light waves that will be 2 wavelengths farther from the central antinide. As you move to slits farther and farther from the center, the path lengths will increase by 3 wavelengths, 4 wavelengths, 5 wavelengths etc. from the central antinode.
Actually the speed of light is ALWAYS 3.0 x 10^8 m/sec! What is actually called the speed of light is actually the "propagation velocity" which includes the absorption and re-emission of light as it passes through the medium! The speed of light is always the same!
A prism separates light into its component colors because the different angles and their effect on the light entering and exiting the prism. In the case of a semi-circular disk the light will intersect the curved surface nearly perpendicularly to the surface.